Related papers: Hybrid Generative Modeling for Incomplete Physics:…

Diffusion models have recently outperformed alternative approaches to model the distribution of natural images, such as GANs. Such diffusion models allow for deterministic sampling via the probability flow ODE, giving rise to a latent space…

In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…

Imbalanced data pose challenges for deep learning based classification models. One of the most widely-used approaches for tackling imbalanced data is re-weighting, where training samples are associated with different weights in the loss…

This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…

Diffusion Models (DMs) have achieved remarkable progress in generative modeling. However, the mismatch between the forward terminal distribution and reverse initial distribution introduces prior error, leading to deviations of sampling…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…

Graph Neural Networks (GNNs) with equivariant properties have achieved significant success in modeling complex dynamic systems and molecular properties. However, their expressiveness ability is limited by: (1) Existing methods often…

Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…

Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT…

Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of…

Estimating reaction rates and chemical stability is fundamental, yet efficient methods for large-scale simulations remain out of reach despite advances in modeling and exascale computing. Direct simulation is limited by short timescales;…

In the quest for controlled thermonuclear fusion, tokamaks present complex challenges in understanding burning plasma dynamics. This study introduces a multi-region multi-timescale transport model, employing Neural Ordinary Differential…

Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previous studies, OT has…

We introduce optimal transport (OT) as a physics-based intermediate event representation for weakly supervised anomaly detection. With only $0.5\%$ injection of resonant signals in the LHC Olympics benchmark datasets, the OT-augmented…

Many existing transductive bounds rely on classical complexity measures that are computationally intractable and often misaligned with empirical behavior. In this work, we establish new representation-based generalization bounds in a…

Conventional Knowledge Graph Completion (KGC) assumes that all test entities appear during training. However, in real-world scenarios, Knowledge Graphs (KG) evolve fast with out-of-knowledge-graph (OOKG) entities added frequently, and we…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…